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Analytic solution of certain second-order functional differential equation. (English) Zbl 1144.34042

The authors are concerned with existence of analytic solutions to certain class of more general iterative second-order functional differential equations. The article by J.-G. Si and X.-P.Wang [Comput. Math. Appl. 43, No. 1–2, 81–90 (2002; Zbl 1008.34059)] is the main reference in this paper.

MSC:

34K05 General theory of functional-differential equations

Citations:

Zbl 1008.34059
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Full Text: DOI

References:

[1] M. Kuczma, Functional Equations in a Single Variable, Monografie Matematyczne, Tom 46, Polish Scientific, Warszawa, 1968. · Zbl 0196.16403
[2] J.-G. Si and X.-P. Wang, “Analytic solutions of a second-order iterative functional differential equation,” Journal of Computational and Applied Mathematics, vol. 126, no. 1-2, pp. 277-285, 2000. · Zbl 0983.34056 · doi:10.1016/S0377-0427(99)00359-3
[3] J.-G. Si and X.-P. Wang, “Analytic solutions of a second-order iterative functional differential equation,” Computers & Mathematics with Applications, vol. 43, no. 1-2, pp. 81-90, 2002. · Zbl 1008.34059 · doi:10.1016/S0898-1221(01)00273-5
[4] J.-G. Si, X.-P. Wang, and S. S. Cheng, “Analytic solutions of a functional-differential equation with a state derivative dependent delay,” Aequationes Mathematicae, vol. 57, no. 1, pp. 75-86, 1999. · Zbl 0959.34061 · doi:10.1007/s000100050071
[5] J.-G. Si, X.-P. Wang, and W.-N. Zhang, “Analytic invariant curves for a planar map,” Applied Mathematics Letters, vol. 15, no. 5, pp. 567-573, 2002. · Zbl 1088.37507 · doi:10.1016/S0893-9659(02)80008-8
[6] J.-G. Si and W. Zhang, “Analytic solutions of a nonlinear iterative equation near neutral fixed points and poles,” Journal of Mathematical Analysis and Applications, vol. 284, no. 1, pp. 373-388, 2003. · Zbl 1030.39025 · doi:10.1016/S0022-247X(03)00363-9
[7] J.-G. Si and W. Zhang, “Analytic solutions of a class of iterative functional differential equations,” Journal of Computational and Applied Mathematics, vol. 162, no. 2, pp. 467-481, 2004. · Zbl 1044.34020 · doi:10.1016/j.cam.2003.08.049
[8] J.-G. Si and W. Zhang, “Analytic solutions of a second-order nonautonomous iterative functional differential equation,” Journal of Mathematical Analysis and Applications, vol. 306, no. 2, pp. 398-412, 2005. · Zbl 1083.34060 · doi:10.1016/j.jmaa.2005.01.005
[9] J.-G. Si, W. Zhang, and G.-H. Kim, “Analytic solutions of an iterative functional differential equation,” Applied Mathematics and Computation, vol. 150, no. 3, pp. 647-659, 2004. · Zbl 1040.34525 · doi:10.1016/S0096-3003(03)00296-0
[10] X.-P. Wang and J.-G. Si, “Analytic solutions of an iterative functional differential equation,” Journal of Mathematical Analysis and Applications, vol. 262, no. 2, pp. 490-498, 2001. · Zbl 1001.34055 · doi:10.1006/jmaa.2001.7527
[11] B. Xu, W. Zhang, and J.-G. Si, “Analytic solutions of an iterative functional differential equation which may violate the Diophantine condition,” Journal of Difference Equations and Applications, vol. 10, no. 2, pp. 201-211, 2004. · Zbl 1057.34067 · doi:10.1080/1023-6190310001596571
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